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Axiom ax-addcl 9010
Description: Closure law for addition of complex numbers. Axiom 4 of 22 for real and complex numbers, justified by theorem axaddcl 8986. Proofs should normally use addcl 9032 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )

Detailed syntax breakdown of Axiom ax-addcl
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 8948 . . . 4  class  CC
31, 2wcel 1721 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1721 . . 3  wff  B  e.  CC
63, 5wa 359 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 8953 . . . 4  class  +
81, 4, 7co 6044 . . 3  class  ( A  +  B )
98, 2wcel 1721 . 2  wff  ( A  +  B )  e.  CC
106, 9wi 4 1  wff  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )
Colors of variables: wff set class
This axiom is referenced by:  addcl  9032
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